Negative form and て行く (maybe て-form in general)

Question

Sentence: 「おや、Xさん。テストの結果が貼りだされているというのに見て行かなくていいんですか？」

How 見ていく is used here is confounding me. 見て行く would be something like "see the test result and then go his way". I understand that what this character wants to ask is "Even though the results have already been posted, is it okay to not give them a look (before going away)". However, why is the 行く in negative form and not 見る?

The thing the person will leave without doing is "seeing". Would it be wrong to say 「（…）見ないで行ってもいいんですか？」? Or 「見に行かなくていいんですか？」?

There's been repeated instances of an unexpected part of a sentence with the て-form going into the negative (usually the last verb) and catching me off-guard as it seems to negate the whole sequence of verbs. In a sentence with the te-form, if the last verb is negative, does that negation include the verb in the て-form as well? Or does it happen here because 見て行く(the kanji is utilized in the source as well, which made me think it was to emphasize separate actions: 見る and then 行く) is treated differently?

Answer 1

As you interpret, 見て行く means see sth here before go away. 見て行く works like one word, so negating ない could be added after it. e.g.見ていかなくてもいいの

But also you can divide it and say 見ないで行ってもいいの.

For me 見て行かなくても sounds by far more natural but 見ないで行っても would be barely OK.